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Work47

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Aaron Anderson1
Aaron Frank1
Aaron Litoff1
Alex Valdes1
Alexandra Rodriguez1
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Keyword

Optimization9
Game Theory3
Interior Point2
Absolute Values1
Adaptive Robust Optimization1
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Process Optimization[remove]47

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Featured Applications - Wing Shape Optimization

Description:

Aerospace collectively represents one of the most sophisticated technological endeavors and largest markets in the world. Coming with substantial costs, nearly every aspect of the industry, from aircraft design to material selection to operation, has been optimized in at least one way. A critical design consideration in any aircraft is...

Keyword:

Wingshape and Optimization

Creator:

Daniel Charles

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Featured Applications - Applying Optimization in Game Theory

Description:

Optimization and Game Theory have certain conceptual overlaps. It is even said that John von Neumann conjectured the Duality Theorem using information from his game theory. This article discusses two optimization applications to the game theory: a methodology for solving the Nash Equilibrium and a decentralized model in supply chain...

Keyword:

Game Theory and Optimization

Creator:

Leon Huang

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Global Optimization - Exponential transformation

Description:

This article concerns the exponential transformation method for globally solving posynomial (or general geometric/signomial) optimization problems with nonconvex objective functions or constraints. A discussion of the method's development and use will be presented.

Keyword:

Exponential Transformation and Optimization

Creator:

Daniel Garcia

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Global Optimization - Logarithmic Transformation

Description:

Logarithmic transformation is a method used to change geometric programs into their convex forms. A geometric program, or GP, is a type of global optimization problem that concerns minimizing a subject to constraint functions so as to allow one to solve unique non-linear programming problems. All geometric programs contain functions...

Keyword:

Logarithmic and Transformation

Creator:

Hassan Ali

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Global Optimization - McCormick Envelopes

Description:

McCormick Envelopes are a type of convex relaxation used in bilinear Non Linear Programming problems. Many times these envelopes are used to solve a Mixed Integer Non Linear Programming problem by relaxing the MINLP problem so that it becomes a convex NLP. Solving this convex NLP will provide a lower...

Keyword:

Global Optimization and McCormick

Creator:

John Dombrowski

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Global Optimization - Piecewise linear approximation

Keyword:

Linear Approximation, Optimization, and Piecewise

Creator:

John Marsiglio

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Global Optimization - Spatial branch and bound method

Description:

Spatial branch-and-bound is a divide-and-conquer technique used to find the deterministic solution of global optimization problems.1 It is a type of branch-and-bound method, which solves for the set of parameters that globally optimize the objective function, whether that be finding the minimum or maximum value of or , respectively, where...

Keyword:

Bound and Spatial Branch

Creator:

Ellen Zhuang

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Linear Programming - Computational complexity

Description:

Computational complexity refers to the amount of resources required to solve a type of problem by systematic application of an algorithm. Resources that can be considered include the amount of communications, gates in a circuit, or the number of processors. Because the size of the particular input to a problem...

Keyword:

Computational and Complexity

Creator:

David O'Brien, Mark Caswell, and David Chen

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Linear Programming - Matrix game

Description:

The objective of game theory is to analyze the relationship between decision-making situations in order to achieve a desirable outcome. The theory can be applied to a wide range of applications, including, but not limited to, economics, politics and even the biological sciences. In essence, game theory serves as means...

Keyword:

Game Theory, Matrices, and Matrix

Creator:

Matt Kweon and Nick Dotzenrod

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Linear Programming - Network flow problem

Description:

Network Flow Optimization problems form the most special class of linear programming problems. Transportation, electric, and communication networks are clearly common applications of Network Optimization. These types of problems can be viewed as minimizing transportation problems. This Network problem will include cost of moving materials through a network involving varying...

Keyword:

Network Flow and Linear Programming

Creator:

Aaron Frank, Blake Alexander, and Joshua Lee

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Linear Programming - Interior-point method

Description:

Interior point methods are a type of algorithm that are used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The LP Interior-Point method relies on having a linear programming model with the objective function and all constraints being continuous and twice continuously differentiable. In...

Keyword:

Interior Point

Creator:

John Plaxco, Alex Valdes, and Wojciech Stojko

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Linear Programming - Optimization with absolute values

Description:

Optimization with absolute values is a special case of linear programming in which a problem made nonlinear due to the presence of absolute values is solved using linear programming methods. Absolute value functions themselves are very difficult to perform standard optimization procedures on. They are not continuously differentiable functions, are...

Keyword:

Absolute Values and Optimization

Creator:

Benjamin Granger, Kathleen Zhou, and Marta Yu

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Facility location problems

Description:

Facility location problems deal with selecting the placement of a facility (often from a list of integer possibilities) to best meet the demanded constraints. The problem often consists of selecting a factory location that minimizes total weighted distances from suppliers and customers, where weights are representative of the difficulty of...

Keyword:

Mixed-Integer Linear Programming and Facility

Creator:

Aaron Litoff

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Traveling salesman problems

Description:

The traveling salesman problem (TSP) is a widely studied combinatorial optimization problem, which, given a set of cities and a cost to travel from one city to another, seeks to identify the tour that will allow a salesman to visit each city only once, starting and ending in the same...

Keyword:

Game Theory and Travelling Salesman

Creator:

Jessica Yu

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Mixed-Integer Cuts

Description:

Mixed-integer cuts or Cutting-plane methods is an iterative approach used to simplify the solution of a mixed integer linear programming (MILP) problem. Cutting-plane methods work by first relaxing the MILP to a complementary linear programming problem and cutting the feasible region to narrow down the solution search space to only...

Keyword:

Mixed-integer and linear programming

Creator:

Tahir Kapoor

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Disjunctive inequalities

Description:

A disjunctive inequality is a type of constraint that exists in mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) problems. It involves constraining a solution space with multiple inequalities or sets of inequalities related by an OR statement. This "OR" statement must then be reformulated using one...

Keyword:

Disjunctive inequalities

Creator:

Camille Bilodeau

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Column generation algorithms

Description:

Column generation algorithms are used for MILP problems. The formulation was initially proposed by Ford and Fulkerson in 1958 . The main advantage of column generation is that not all possibilities need to be enumerated. Instead, the problem is first formulated as a restricted master problem (RMP). This RMP has...

Keyword:

Column Generations and Algorithms

Creator:

Kedric Daly

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Heuristic algorithms

Description:

A heuristic algorithm is one that is designed to solve a problem in a faster and more efficient fashion than traditional methods by sacrificing optimality, accuracy, precision, or completeness for speed. Heuristic algorithms often times used to solve NP-complete problems, a class of decision problems. In these problems, there is...

Keyword:

Heuristic

Creator:

Vincent Kenny, Matthew Nathal, and Spencer Saldana

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Branch and Cut

Description:

Branch and cut method is a very successful algorithm for solving a variety of integer programming problems, and it also can provide a guarantee of optimality. Many problems involve variables which are not continuous but instead have integer values, and they can be solved by branch-and cut method. This method...

Keyword:

Cut, Mixed-Linear Programming, and Branch

Creator:

YenChieh Chou

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/29/2018
Mixed-Integer Linear Programming: Lagrangean duality

Description:

Lagrangian duality theory refers to a way to find a bound or solve an optimization problem (the primal problem) by looking at a different optimization problem (the dual problem). More specifically, the solution to the dual problem can provide a bound to the primal problem or the same optimal solution...

Keyword:

Lagrangian and Duality

Creator:

Hannah Seo

Owner:

Scholarly Digital Publishing

Date Uploaded:

11/29/2018

Date Modified:

11/30/2018

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